"My Moon"

To say 'my moon' as an endearment, would you say 'moya luna' (моя луна) or 'luna moya', (луна моя)?

Eh... Technically either. I suppose моя луна is preferred. It's not really too important.

In Russian word order is not fixed. So the positions of noun and pronoun are interchangable here. But more importantly, this term of endearment is not used in Russian)... sorry about that) ... Is it really used in English as term of endearment?

But the poetic simile can be used.. e.g. Вы как блестящая луна (you are like a moon)...

As endearment, we often use such a technique (observe the unusual word order):

<something> ты [мой] <epithet> !

For example:
Солнышко ты моё светлое!
Ягодка ты моя волчья! (evil joke)

Also look at this:
Киркоров Филипп «Зайка моя» - текст и слова песни в караоке на karaoke.ru

In short, you usually add "ты" somewhere and then it's not very important, be it
ты моя луна
луна ты моя
моя ты луна
ты луна моя
...
Different intonations apply, though!

Thank you all for your help! And no, Alexsms, 'my moon' isn't often used in English either, but I'm writing a book, and in the context of the story it makes sense as an endearment :)